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Spectrum of the complex Laplacian on product domains

We show that the spectrum of the complex Laplacian on a product of hermitian manifolds is the Minkowski sum of the spectra of the complex Laplacians on the factors. We use this fact to show that the range of the d-bar operator on a product manifold is closed, provided it is closed in each factor.

preprint2010arXivOpen access
Debraj Chakrabarti
math.CVmath.SP
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Debraj Chakrabarti

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